A method for detecting a tilt angle crystal interface

Abstract

The present application relates to a method for detecting the tilt angle of a crystal interface, comprising the following steps: S1. obtaining a bonded crystal by bonding a top crystal and a bottom crystal, preparing TEM lamellae on the bottom surface of the top crystal and the top surface of the bottom crystal respectively, and obtaining two cross-sectional TEM lamellae; S2. determining the interface AOC and the interface BOD on the contact surfaces of the two TEM lamellae respectively, establishing a Cartesian three-dimensional coordinate system according to the interface AOC and the interface BOD, recording the included angle AOB as θ1, the included angle COD as θ2, and the included angle BOD as θ3, measuring and recording θ1, θ2 and θ3; S3. calculating the tilt angle θ0 of the interface AOC and the interface BOD according to θ1, θ2 and θ3, and obtaining the tilt angle of the bonded crystal. By preparing TEM lamellae on the bonding interface of the bonded crystal and measuring multiple included angles in the three-dimensional coordinate system, the geometric relationship of the crystal interface is modeled, and the tilt angle of the interface is calculated with high precision.

Description

Technical Field

[0001] This invention relates to the field of crystal detection technology, and more specifically to a method for detecting the interface of a tilted crystal. Background Technology

[0002] The atomic arrangement at the heterojunction interface determines the physical and chemical properties of the crystalline composite material. Aberration-corrected transmission electron microscopy (Ac-TEM) allows for direct observation and analysis of the crystallographic information of heterojunction materials, including the arrangement of bulk atoms, the types of atoms, and the bonding patterns of interface atoms. A schematic diagram of a tilted crystal interface is shown below. Figure 1 As shown. The tilt axis of the heterojunction is a line in three-dimensional space, for example, below. Figure 1 The tilt axis of the interface is a line perpendicular to the image plane.

[0003] In actual testing, it is often difficult to predict the position and orientation of the crystal interface tilt axis in three-dimensional space, making it impossible to directly and accurately measure the tilt angle. Observing the tilt angle from a random direction in three-dimensional space will lead to inaccurate measurement values. Summary of the Invention

[0004] Based on the above description, the present invention provides a method for detecting the tilt angle of a crystal interface, which aims to solve the problem of low accuracy in detecting the tilt angle of the interface of bonded crystals.

[0005] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0006] This invention provides a method for detecting tilted crystal interfaces, comprising the following steps:

[0007] S1. Obtain the bonded crystal obtained by bonding the top crystal and the bottom crystal, and prepare TEM thin films on the bottom surface of the top crystal and the top surface of the bottom crystal respectively to obtain two cross-sectional TEM thin films with different directions;

[0008] S2. Determine the interface AOC and interface BOD on the contact surfaces of the two TEM sheets respectively. Establish a Cartesian three-dimensional coordinate system based on the interface AOC and interface BOD. Denote the included angle AOB as θ1, the included angle COD as θ2, and the included angle BOD as... Measure and record θ1, θ2 and ;

[0009] S3. Based on θ1, θ2 and The tilt angle θ0 of the interface AOC and interface BOD is calculated to obtain the tilt angle of the bonded crystal.

[0010] Furthermore, in step S2, θ1, θ2, and θ3 are measured and recorded. When using this method, any one of TEM, STEM, EBSD, CBED, Kikuchi Pattern, NBD, PED, Moiré Pattern, and 4D-STEM can be used for detection.

[0011] Furthermore, in step S2, when establishing the Cartesian three-dimensional coordinate system, a three-dimensional rectangular coordinate system is established with the line containing OB as the x-axis, the plane containing the included angle AOB as the xz plane, and the plane containing the included angle BOD as the xy plane.

[0012] Furthermore, step S3 includes:

[0013] S31. Let the unit vector on line OB be... a 1. The unit vector on line OA is a 2. The unit vector on the OD line is b 1. The unit vector on line OC is b 2. The normal vector of the interface AOC is c 1. The normal vector of the interface BOD is c 2;

[0014] S32. Based on vector a 1. a 2. b 1. b 2. c 1. c 2 and θ1, θ2 and The mathematical relationship between them is expressed by θ1, θ2 and θ3. The tilt angle θ0 of the interface AOC and interface BOD is used to obtain the tilt angle of the bonded crystal.

[0015] Furthermore, step S32 includes the following steps:

[0016] Let the unit vector on line OB be... a 1. As shown in equation (1),

[0017] (1),

[0018] Will a 1. Rotate θ1 around the y-axis to obtain a 2. As shown in equation (2),

[0019] (2),

[0020] Will a 1. Rotate about the z-axis ,get b 1. As shown in equation (3),

[0021] (3),

[0022] according to b 1. Calculate the normal vector of the plane containing the angle COD. u 1. As shown in equation (4),

[0023] (4),

[0024] Will b 1 with u 1. Rotate the axis of rotation by θ2 to obtain... b 2. Calculate according to Rodrigues' formula in equation (5) b 2, of which I It is the identity matrix. R k for u The antisymmetric matrix of 1 and its matrix vector are shown in equation (6), which are calculated using equations (5) and (6). b 2. As shown in equation (7),

[0025] (5),

[0026] (6),

[0027] (7),

[0028] According to the vector a 1. a 2. b 1 and b 2. Calculate the normal vector of interface AOC. c 1. Normal vector of the interface BOD c 2. As shown in equations (8) and (9),

[0029] (8),

[0030] (9),

[0031] According to the vector c 1 and c 2. The tilt angle θ0 of interfaces AOC and BOD is calculated as shown in equations (10) and (11).

[0032] (10)

[0033] (11).

[0034] Furthermore, step S32 also includes:

[0035] S33. Based on vector c 1 and c The 2-cross product yields the slant axis vector. u 2.

[0036] Furthermore, in step S33, the tilt axis vector u The formula for calculating 2 is shown in equation (12).

[0037] (12).

[0038] Furthermore, at the included angle When =π / 2, u 2. As shown in equation (13),

[0039] (13).

[0040] Furthermore, step S33 also includes:

[0041] S34. Based on the tilt axis vector u 2. Locate the tilt axis of the bonded crystal, extract a TEM thin section perpendicular to the tilt axis, and observe the interface tilt angle of the bonded crystal.

[0042] Furthermore, step S3 also includes:

[0043] S4. Determine another pair of interfaces on the contact surfaces of the two TEM sheets, establish a Cartesian three-dimensional coordinate system based on the two interfaces, measure and record the included angles between the sides of the interfaces, calculate the tilt angle between the interfaces based on the included angles between the sides, and calculate the tilt angle of the bonded crystal with the tilt angle θ0.

[0044] Compared with the prior art, the technical solution of this application has the following beneficial technical effects:

[0045] (1) By preparing TEM thin films at the bonding interface of the top crystal and the bottom crystal respectively, and measuring multiple key angles in the three-dimensional coordinate system, the geometric relationship of the crystal interface can be accurately modeled, thereby realizing the high-precision quantitative calculation of the interface tilt angle, overcoming the problem of insufficient accuracy of traditional analysis methods. This method is not only applicable to ideally aligned crystal bonding, but also effectively evaluates tilted interfaces caused by processing deviations or lattice mismatch.

[0046] (2) By introducing unit vectors a 1. a 2. b 1. b 2 and normal vector c 1. c 2. Construct a complete 3D geometric model so that the interface tilt angle θ0 can be accurately solved through vector operations; through normal vectors...c 1. c 2. Directly calculate the dihedral angle θ0 between the two interfaces. The physical meaning is clear and the result is unique. This avoids the error caused by the uncertainty of the projection direction in traditional measurement, and significantly improves the reliability of the result and the accuracy of the calculation.

[0047] (3) Through calculation c 1× c 2. Obtain the tilt axis vector u 2. It accurately characterizes the rotation axis direction of the relative tilt between two crystal interfaces, achieving a complete description of the spatial orientation relationship of the interface; combining the magnitude of the tilt angle θ0 and the tilt axis vector u 2. A complete three-dimensional geometric model of the bonding interface was constructed, providing key structural parameters for device performance analysis. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of a single-TEM sample detection method in the prior art. Figure 1 Image (a) in the diagram is a schematic diagram of cross-sectional TEM (XTEM) sample preparation. Figure 1 (b) in the diagram is a schematic diagram of TEM measurement of the tilt angle. Figure 1 (c) in the diagram is a schematic diagram of the FIB slice and the TEM observation direction. Figure 1 (d) in the diagram illustrates the influence of the observation direction on the measurement results;

[0049] Figure 2 This is a schematic diagram of existing crystal interface detection methods based on small-angle grain boundaries and planar TEM (PVTEM) technology. Figure 2 (a) in the diagram is a schematic diagram of the sample preparation method. Figure 2 (b) in the figure is a schematic diagram of the grid-like and banded stripes obtained by TEM imaging;

[0050] Figure 3 This is a schematic diagram illustrating the measurement of the tilt angle in one embodiment of the tilt angle crystal interface detection method of the present invention;

[0051] Figure 4 for Figure 1 A schematic diagram of the crystal interface constructed in coordinates. Detailed Implementation

[0052] To facilitate understanding of this application, a more complete description will be provided below with reference to the accompanying drawings, which illustrate embodiments of the present application. However, the present application can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided so that the disclosure of this application will be thorough and complete.

[0053] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0054] The atomic arrangement at the heterojunction interface determines the physical and chemical properties of the crystalline composite material. Aberration-corrected transmission electron microscopy (Ac-TEM) allows for direct observation and analysis of the crystallographic information of heterojunction materials, including the arrangement of bulk atoms, the types of atoms, and the bonding patterns of interface atoms. A schematic diagram of a tilted crystal interface is shown below. Figure 1 As shown. The tilt axis of the heterojunction is a line in three-dimensional space, for example, below. Figure 1 The tilt axis of the interface is a line perpendicular to the image plane.

[0055] Existing TEM testing techniques for crystal interface tilt angles typically employ cross-sectional TEM sample methods or methods based on small-angle grain boundaries and PVTEM.

[0056] In single TEM sample detection methods, the sample preparation direction is perpendicular to the crystal interface, such as... Figure 1 As shown in (a), the TEM slice protrudes in a direction perpendicular to the image plane. The resulting TEM slice contains three parts: the top crystal, the interface, and the bottom crystal. The tilt angle θ of the crystal interface is measured using TEM imaging. TEM imaging can employ techniques such as real-space imaging (TEM, HRTEM, STEM-HAADF / BF) or inverted-space imaging (SAED, CBD, NBD, PED, Kikuchi Pattern). Figure 1 As shown in (b), the interface tilt angle θ is measured by analyzing the crystallographic information of the top and bottom crystals or the crystal interface. Here, the crystallographic information refers to crystal planes or crystal orientations.

[0057] Under ideal testing conditions, the e-beam direction of the TEM is parallel to the Tilt axis direction of the crystal interface, such as... Figure 1 As shown in (c). The intersection line Tilt axis of the top and bottom crystals is defined as the x-axis direction, and the e-beam direction of the TEM is parallel to the x-axis. Since TEM imaging is a projection image, the A'O'B' obtained by TEM is an accurate value, i.e., A'O'B' = AOB = θ. A line OA and OB parallel to the yz plane of the Cartesian coordinate system tangent to the bottom surface of the top crystal and the top surface of the bottom crystal.

[0058] However, achieving the above ideal conditions in actual testing requires prior knowledge of the position or orientation of the titrating axis in the 3D space of the sample, and fixing the sample extraction orientation during TEM sample preparation. Failure to predict the titrating axis at the crystal interface and performing TEM slicing and AOB observation in a random orientation will lead to inaccurate test results. Figure 2 As shown in (d), observing AOB from a random position is equivalent to rotating the sample around the x, y, or z axes while keeping the observation direction unchanged. In the diagram, we fix point O and rotate the sample. When AOB rotates around the x-axis, the measured angle θ' is the accurate tilt angle, θ' = θ; when sample AOB rotates around the y-axis, the measured angle θ' < θ; when sample AOB rotates around the z-axis, the measured angle θ' > θ, θ' = C'O'D'. The figure illustrates the situation when sample AOB rotates around the z-axis. Analysis shows that, without knowing the position and direction of the Tilt axis at the crystal interface, only random positions can be extracted for TEM slices and measurements, resulting in inaccurate results. Preparing a randomly segmented TEM sample cannot accurately measure the tilt angle.

[0059] In crystal interface detection methods based on small-angle grain boundaries and PVTEM, the small-angle grain boundary theory posits that crystal interfaces consist of periodic dislocation distributions, including Tilt Interfacial Dislocations (TIDs). In TEM imaging, TIDs form banded moiré patterns, such as... Figure 2 As shown in (b) above, the spacing between the moiré stripe bands formed by TIDs exhibits a Frank relationship with the Tilt angle of the crystal interface: , where b is the size of the Burgers vector of the dislocation, and θ is the Tilt angle of the crystal interface.

[0060] Sample preparation, such as Figure 3 As shown in (a), PVTEM thin films are prepared using mechanical methods, Ion Milling, Dimple, or FIB techniques. The thin films need to contain a top crystal, an interface, and a bottom crystal.

[0061] Thin-section samples are imaged using TEM to resolve the moiré fringe patterns formed by periodic dislocations, and the average distance between adjacent TIDs (Transient Identifiers) (DTIDs) is measured. The interface tilt angle θ is calculated using the Frank relation formula, combined with the material's lattice parameters. This method is only applicable when the atomic arrangement at the interface satisfies a small-angle grain boundary structure, and the analysis must ensure that the TEM image clearly shows the continuous distribution of TIDs to guarantee measurement accuracy.

[0062] Therefore, cross-sectional TEM testing is generally applicable to various interfacial atomic arrangements. However, in actual testing, it is difficult to predict the position and orientation of the crystal interface tilt axis in three-dimensional space. Single-section TEM sampling methods result in the inability to directly and accurately measure the tilt angle, and testing methods based on small-angle boundary theory are not applicable when the interface is not periodically displaced. Observing the tilt angle from random directions in three-dimensional space leads to inaccurate measurement values.

[0063] In view of this, see Figure 4 This invention provides a method for detecting tilt angle crystal interfaces, comprising the following steps:

[0064] S1. Obtain the bonded crystal obtained by bonding the top crystal and the bottom crystal, and prepare TEM thin films on the bottom surface of the top crystal and the top surface of the bottom crystal respectively to obtain two cross-sectional TEM thin films with different directions;

[0065] S2. Determine the interface AOC and interface BOD on the contact surfaces of the two TEM sheets respectively. Establish a Cartesian three-dimensional coordinate system based on the interface AOC and interface BOD. Denote the included angle AOB as θ1, the included angle COD as θ2, and the included angle BOD as... Measure and record θ1, θ2 and ;

[0066] S3. Based on θ1, θ2 and The tilt angle θ0 of the interface AOC and interface BOD is calculated to obtain the interface tilt angle of the bonded crystal.

[0067] In the technical solution of this invention, TEM thin films are prepared at the bonding interfaces of the top and bottom crystals, and multiple key angles are measured in a three-dimensional coordinate system. This enables precise modeling of the geometric relationship of the crystal interface, thereby achieving high-precision quantitative calculation of the interface tilt angle and overcoming the problem of insufficient accuracy in traditional analysis methods. This method is not only applicable to ideally aligned crystal bonding, but can also effectively evaluate tilted interfaces caused by processing deviations or lattice mismatches.

[0068] Specifically, in the technical solution of this invention, the interface AOC and the interface BOD are mutually projected interfaces, that is, the projection of AOC onto the interface where BOD is located coincides with BOD, and the projection of BOD onto the interface where AOC is located coincides with AOC, thereby constructing a reversible three-dimensional interface model, which improves the accuracy of detecting the tilt angle of the crystal bonding interface.

[0069] It should be noted that the crystal interface can be a homogeneous interface or a heterogeneous interface; in step S1, the TEM thin film can be prepared by mechanical grinding, pitting, argon ion beam polishing, or focused ion beam technology, and is not limited here; in step S2, the measurements of θ1, θ2, and The method can be TEM measurement, synchrotron radiation measurement, or atomic probe imaging measurement; no specific method is specified here.

[0070] Furthermore, in step S2, θ1, θ2, and θ3 are measured and recorded. When using this method, any one of TEM, STEM, EBSD, CBED, Kikuchi Pattern, NBD, PED, Moiré Pattern, and 4D-STEM can be used for detection.

[0071] In the technical solution of this invention, by employing the above method, nanometer-level or even atomic-level resolution can be achieved, enabling precise identification of crystal orientation and interface positions, and significantly improving θ1, θ2, and... This improves the measurement accuracy, thereby enhancing the calculation accuracy of the tilt angle θ0. By employing different methods, it is possible to adapt to different crystal materials and sample conditions. Furthermore, during the detection process, multiple methods can be used for cross-validation, further improving the detection accuracy.

[0072] For further details, please refer to [link / reference]. ​ In step S2, when establishing the Cartesian three-dimensional coordinate system, a three-dimensional rectangular coordinate system is established with the line containing OB as the x-axis, the plane containing the included angle AOB as the xz plane, and the plane containing the included angle BOD as the xy plane.

[0073] In the technical solution of this invention, a three-dimensional coordinate system is established through explicit geometric rules, with the common side OB as the x-axis, and the key included angle θ1 (AOB) and The (BOD) is positioned in the xz and xy planes respectively, providing a unified and stable reference frame for angle measurement and reducing human calibration errors.

[0074] Furthermore, step S3 includes:

[0075] S31. Let the unit vector on line OB be... a 1. The unit vector on line OA is a 2. The unit vector on the OD line is b 1. The unit vector on line OC is b 2. The normal vector of the interface AOC is c 1. The normal vector of the interface BOD is c 2;

[0076] S32. Based on vector a 1. a 2.b 1. b 2. c 1. c 2 and θ1, θ2 and The mathematical relationship between them is expressed by θ1, θ2 and θ3. The tilt angle θ0 of the interface AOC and interface BOD is used to obtain the tilt angle of the bonded crystal.

[0077] In the technical solution of this invention, a unit vector is introduced. a 1. a 2. b 1. b 2 and normal vector c 1. c 2. Construct a complete 3D geometric model so that the interface tilt angle θ0 can be accurately solved through vector operations; through normal vectors... c 1. c 2. Directly calculating the dihedral angle θ0 between the two interfaces has a clear physical meaning and a unique result, avoiding the error caused by the uncertainty of the projection direction in traditional measurement, significantly improving the reliability of the result and enhancing the calculation accuracy.

[0078] Furthermore, step S32 includes the following steps:

[0079] Let the unit vector on line OB be... a 1. As shown in equation (1),

[0080] (1),

[0081] Will a 1. Rotate θ1 around the y-axis to obtain a 2. As shown in equation (2),

[0082] (2),

[0083] Will a 1. Rotate about the z-axis ,get b 1. As shown in equation (3),

[0084] (3),

[0085] according to b 1. Calculate the normal vector of the plane containing the angle COD. u 1. As shown in equation (4),

[0086] (4),

[0087] Will b 1 with u 1. Rotate the axis of rotation by θ2 to obtain... b2. Calculate according to Rodrigues' formula in equation (5) b 2, of which I It is the identity matrix. R k for u The antisymmetric matrix of 1 and its matrix vector are shown in equation (6), which are calculated using equations (5) and (6). b 2. As shown in equation (7),

[0088] (5),

[0089] (6),

[0090] (7),

[0091] According to the vector a 1. a 2. b 1 and b 2. Calculate the normal vector of interface AOC. c 1. Normal vector of the interface BOD c 2. As shown in equations (8) and (9),

[0092] (8),

[0093] (9),

[0094] According to the vector c 1 and c 2. The tilt angle θ0 of interfaces AOC and BOD is calculated as shown in equations (10) and (11).

[0095] (10)

[0096] (11).

[0097] Furthermore, step S32 also includes:

[0098] S33. Based on vector c 1 and c The 2-cross product yields the slant axis vector. u 2.

[0099] In the technical solution of this invention, through calculation c 1× c 2. Obtain the tilt axis vector u 2. It accurately characterizes the rotation axis direction of the relative tilt between two crystal interfaces, achieving a complete description of the spatial orientation relationship of the interface; combining the magnitude of the tilt angle θ0 and the tilt axis vector u2. A complete three-dimensional geometric model of the bonding interface was constructed, providing key structural parameters for device performance analysis.

[0100] Furthermore, in step S33, the tilt axis vector u The formula for calculating 2 is shown in equation (12).

[0101] (12).

[0102] Furthermore, at the included angle When =π / 2, u 2. As shown in equation (13),

[0103] (13).

[0104] Furthermore, step S33 also includes:

[0105] S34. Based on the tilt axis vector u 2. Locate the tilt axis of the bonded crystal, extract a TEM thin section perpendicular to the tilt axis, and observe the interface tilt angle of the bonded crystal.

[0106] In the technical solution of the present invention, by u 2. Accurately locate the tilt axis direction and prepare the TEM sample along a plane perpendicular to this axis. Observation under a specific orientation perpendicular to the tilt axis is beneficial for clearly distinguishing lattice fringes or diffraction spots, facilitating accurate measurement of the actual tilt angle, and enabling experimental verification of the calculated tilt angle θ0. The spatial transformation calculation results are then used to further verify this. u 2. The results are corroborated by actual TEM observations, further improving the accuracy of tilt angle detection.

[0107] Furthermore, step S3 also includes:

[0108] S4. Determine another pair of interfaces on the contact surfaces of the two TEM sheets, establish a Cartesian three-dimensional coordinate system based on the two interfaces, measure and record the included angles between the sides of the interfaces, calculate the tilt angle between the interfaces based on the included angles between the sides, and calculate the tilt angle of the bonded crystal with the tilt angle θ0.

[0109] In the technical solution of the present invention, by measuring multiple interface groups at different locations, tilt information of the bonding interface over a larger range is obtained, avoiding the randomness of single-point measurement and more realistically reflecting the tilt state of the overall interface; by comprehensively evaluating the tilt angles calculated from multiple groups (e.g., taking the average value), random errors can be effectively reduced and the accuracy and repeatability of the final tilt angle result can be improved.

[0110] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0111] In summary, the technical solution of this application has the following beneficial technical effects:

[0112] (1) By preparing TEM thin films at the bonding interface of the top crystal and the bottom crystal respectively, and measuring multiple key angles in the three-dimensional coordinate system, the geometric relationship of the crystal interface can be accurately modeled, thereby realizing the high-precision quantitative calculation of the interface tilt angle, overcoming the problem of insufficient accuracy of traditional analysis methods. This method is not only applicable to ideally aligned crystal bonding, but also effectively evaluates tilted interfaces caused by processing deviations or lattice mismatch.

[0113] (2) By introducing unit vectors a 1. a 2. b 1. b 2 and normal vector c 1. c 2. Construct a complete 3D geometric model so that the interface tilt angle θ0 can be accurately solved through vector operations; through normal vectors... c 1. c 2. Directly calculate the dihedral angle θ0 between the two interfaces. The physical meaning is clear and the result is unique. This avoids the error caused by the uncertainty of the projection direction in traditional measurement, and significantly improves the reliability of the result and the accuracy of the calculation.

[0114] (3) Through calculation c 1× c 2. Obtain the tilt axis vector u 2. It accurately characterizes the rotation axis direction of the relative tilt between two crystal interfaces, achieving a complete description of the spatial orientation relationship of the interface; combining the magnitude of the tilt angle θ0 and the tilt axis vector u 2. A complete three-dimensional geometric model of the bonding interface was constructed, providing key structural parameters for device performance analysis.

Claims

1. A method for detecting the tilt angle of a crystal interface, characterized in that, Includes the following steps: S1. Obtain the bonded crystal obtained by bonding the top crystal and the bottom crystal, and prepare TEM thin films on the bottom surface of the top crystal and the top surface of the bottom crystal respectively to obtain two cross-sectional TEM thin films with different directions; S2. Determine the interface AOC and interface BOD on the contact surfaces of the two TEM sheets respectively. Establish a Cartesian three-dimensional coordinate system based on the interface AOC and interface BOD. Denote the included angle AOB as θ1, the included angle COD as θ2, and the included angle BOD as... Measure and record θ1, θ2 and ; S3. Based on θ1, θ2 and The tilt angle θ0 of the interface AOC and interface BOD is calculated to obtain the interface tilt angle of the bonded crystal.

2. The method for detecting tilt angle crystal interfaces according to claim 1, characterized in that, In step S2, θ1, θ2 and θ3 are measured and recorded. When using this method, any one of TEM, STEM, EBSD, CBED, Kikuchi Pattern, NBD, PED, Moiré Pattern, and 4D-STEM can be used for detection.

3. The method for detecting the tilt angle crystal interface according to claim 1, characterized in that, In step S2, when establishing the Cartesian three-dimensional coordinate system, a three-dimensional rectangular coordinate system is established with the line containing OB as the x-axis, the plane containing the included angle AOB as the xz plane, and the plane containing the included angle BOD as the xy plane.

4. The method for detecting the tilt angle crystal interface according to claim 3, characterized in that, Step S3 includes: S31. Let the unit vector on line OB be... a 1. The unit vector on line OA is a 2. The unit vector on the OD line is b 1. The unit vector on line OC is b 2. The normal vector of the interface AOC is c 1. The normal vector of the interface BOD is c 2; S32. Based on vector a 1. a 2. b 1. b 2. c 1. c 2 and θ1, θ2 and The mathematical relationship between them is expressed by θ1, θ2 and θ3. The tilt angle θ0 of the interface AOC and interface BOD is used to obtain the tilt angle of the bonded crystal.

5. The method for detecting tilt angle crystal interfaces according to claim 4, characterized in that, Step S32 includes the following steps: Let the unit vector on line OB be... a 1. As shown in equation (1), （1）， Will a 1. Rotate θ1 around the y-axis to obtain a 2. As shown in equation (2), （2）， Will a 1. Rotate about the z-axis ,get b 1. As shown in equation (3), （3）， according to b 1. Calculate the normal vector of the plane containing the angle COD. u 1. As shown in equation (4), （4）， Will b 1 with u 1. Rotate the axis of rotation by θ2 to obtain... b 2. Calculate according to Rodrigues' formula in equation (5) b 2, of which I It is the identity matrix. R k for u The antisymmetric matrix of 1 and its matrix vector are shown in equation (6), which are calculated using equations (5) and (6). b 2. As shown in equation (7), （5）， （6）， （7）， According to the vector a 1. a 2. b 1 and b 2. Calculate the normal vector of interface AOC. c 1. Normal vector of the interface BOD c 2. As shown in equations (8) and (9), （8）， （9）， According to the vector c 1 and c 2. The tilt angle θ0 of interfaces AOC and BOD is calculated as shown in equations (10) and (11). （10）， （11）。 6. The method for detecting tilt angle crystal interfaces according to claim 4, characterized in that, Step S32 is followed by: S33. Based on vector c 1 and c The 2-cross product yields the slant axis vector. u 2.

7. The method for detecting tilt angle crystal interfaces according to claim 6, characterized in that, In step S33, the tilt axis vector u The formula for calculating 2 is shown in equation (12). （12）。 8. The method for detecting tilt angle crystal interfaces according to claim 6, characterized in that, At the angle When =π / 2, u 2. As shown in equation (13), （13）。 9. The method for detecting tilt angle crystal interfaces according to claim 6, characterized in that, Step S33 is followed by: S34. Based on the tilt axis vector u 2. Locate the tilt axis of the bonded crystal, extract a TEM thin section perpendicular to the tilt axis, and observe the interface tilt angle of the bonded crystal.

10. The method for detecting tilt angle crystal interfaces according to claim 1, characterized in that, Step S3 is followed by: S4. Determine another pair of interfaces on the contact surfaces of the two TEM sheets, establish a Cartesian three-dimensional coordinate system based on the two interfaces, measure and record the included angles between the sides of the interfaces, calculate the tilt angle between the interfaces based on the included angles between the sides, and calculate the interface tilt angle of the bonded crystal with the tilt angle θ0.

Images